## Kodai Mathematical Journal

- Kodai Math. J.
- Volume 25, Number 2 (2002), 89-107.

### Holomorphic motions in the parameter space for the relaxed Newton's method.

#### Abstract

It is a well known fact, that for certain polynomials $f$ the relaxed Newton's method $N_{f,h}(z) = z - h\frac{f(z)}{f'(z)}$ associated with $f$ has some extraneous attracting cycles. In the case of cubic polynomials the set of these bad conditioned polynomials has been intensively studied and described by means of quasi--holomorphic surgery and holomorphic motions, cf.~\cite{haeseler:1988}. In the present paper we will generalize this description to polynomials of higher degree.

#### Article information

**Source**

Kodai Math. J., Volume 25, Number 2 (2002), 89-107.

**Dates**

First available in Project Euclid: 17 December 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.kmj/1071674434

**Digital Object Identifier**

doi:10.2996/kmj/1071674434

**Mathematical Reviews number (MathSciNet)**

MR2004f:37060

**Zentralblatt MATH identifier**

1016.37020

#### Citation

Kriete, Hartje. Holomorphic motions in the parameter space for the relaxed Newton's method. Kodai Math. J. 25 (2002), no. 2, 89--107. doi:10.2996/kmj/1071674434. https://projecteuclid.org/euclid.kmj/1071674434